We next answer the question of how to obtain \(\phi \) -critical points at least for the case where \(\mathbb {X}\)  is a Hilbert space. Clearly, if \(\mathcal {F}\)  is differentiable then one could consider classical gradient descent methods. Since we are also interested in non-differentiable functions, gradient descent in its classical form may not be applicable. Below we show that a generalized gradient method using relative subgradients instead of gradients will yield \(\phi \) -critical points in the sense of Definition REF . This shows that Algorithm REF  is a natural extension of subgradient descent [1]}, [2]}.
